# Root 2

Hello fellow maths nerds!

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Root 2 is a funny old number. Joined by numbers like Pi and Phi, root 2 is irrational and also quite famous. The principle square root of 2 is roughly equal to 1.41421… and continues without any repetition for infinitely many places. Whats more, this number can be expressed on a piece of paper using only a pencil, an unmarked ruler and a pair of compasses. This was commonly done by the ancient Greeks. The tools stated previously were what they used for the majority of their geometry work, and thanks to Pythagoras and his theorem they were able to construct a line with length root 2.

To the left we have an example of how they achieved this. For a right angled triangle with side lengths of 1 and 1, the hypotenuse is equal to the square root of (1^2 + 1^2), or the square root of 2.

Another use for the square root of 2 is for the silver ratio. The silver ratio is equal to 1 + root 2. The use of this number is more common than you would think, as it is used for the scaling of paper sizes. The proportion of one side to the other is 1 : root 2. If you remove the largest possible square from the rectangle, the proportion becomes 1 : root 2 – 1.